Scaling and thermodynamics of a trapped Bose-condensed gas

TL;DR

This paper explores the thermodynamics of a trapped Bose gas with repulsive interactions, identifying key scaling parameters and calculating thermodynamic functions within the Popov approximation.

Contribution

It introduces a scaling framework for large N Bose gases in harmonic traps and computes relevant thermodynamic functions using the Popov approximation.

Findings

Thermodynamic behavior is governed by two dimensionless parameters.

Scaling functions for condensate fraction, energy, chemical potential, and moment of inertia are derived.

Results provide insights into the effects of interactions and trap deformation on Bose gases.

Abstract

We investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number N of atoms, harmonic oscillator length, deformation of the trap, s-wave scattering length) fix its large N thermodynamic behaviour through two dimensionless scaling parameters. These are the reduced temperature t=T/T^0_c and the ratio \eta between the T=0 value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature T_c^0 of the non-interacting model. The scaling functions relative to the condensate fraction, energy, chemical potential and moment of inertia are calculated within the Popov approximation.